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# First Degree Inequality Examples

### First Degree Inequality Example 1

### First Degree Inequality Example 2

### First Degree Inequality Example 3

- Question
- Solving the first degree inequality - 7x >= 35

- Solution
- A first-degree inequality is an inequality of the form ax + b < 0 ; ax + b > 0
- or ax + b <= 0 ; ax + b >= 0 , where a, b are constant real numbers with a is not zero and x is a veriable.
- ( note: ax + b <= 0 means ax + b is less than or equal to 0 )
- - 7x >= 35 , both sides divide by 7 ,
- obtain -x >= 5 , both sides multiply -1 , obtain x <= -5
- Therefore, the solution is x <= -5
- Note the multiplication properties for inequalities is:
- (i) If a < b and c > 0, then ac < bc
- (ii) If a < b and c < 0, then ac > bc
- That is, when both sides of an inequality multiply a negative number, the inequality changes direction.

- Question
- Solving the first degree inequality 2 ( x + 3 ) < 3 ( x + 1 )

- Solution
- 2 ( x + 3 ) < 3 ( x + 1 )
- 2x + 6 < 3x + 3
- 2x - 3x < - 6 + 3
- - x < - 3 , both sides multiply -1
- x > 3 , therefore, the solution is x > 3

- Question
- Solving the first degree inequality 5 < 3x - 7 < 11

- Solution
- The compound inequality 5 < 3x - 7 < 11 consists of 5 < 3x - 7 and 3x - 7 < 11
- Solving the inequalities:
- case 1:
- 5 < 3x - 7
- move the variable to the left side of the inequality and move the number to the right side of the inequality
- - 3x < - 5 - 7
- - 3x < - 12
- divide by 3 on both side of the inequality
- - x < - 4
- multiply (-1) on both side of the inequality
- x > 4
- note: when both side of the inequality multiply (-1), the inequality change direction.
- case 2:
- 3x - 7 < 11
- move the number to the right side of the inequality
- 3x < 7 + 11
- 3x < 18
- x < 6
- therefore, the solution of the given inequality is: 4 < x < 6
- The solution of the compound inequalities is: 4 < x < 6

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